Abstract. We consider the problem of query evaluation for tuple independent probabilistic databases and Boolean conjunctive queries with inequalities but without self-joins. We approach this problem as a construction problem for ordered binary decision diagrams (OBDDs): Given a query q and a probabilistic database D, we construct in polynomial time an OBDD such that the probability of q(D) can be computed linearly in the size of that OBDD. This approach is applicable to a large class of queries, including the hierarchical queries, i.e., the Boolean conjunctive queries without self-joins that admit PTIME evaluation on any tuple-independent probabilistic database, hierarchical queries extended with inequalities, and non-hierarchical queries on restricted databases. 1

Probabilistic database systems have successfully established themselves as a tool for managing uncertain data. However, much of the research in this area has focused on efficient query evaluation and has largely ignored two key issues that commonly arise in uncertain data management: First, how to provide explanations for query results, e.g., “Why is this tuple in my result? ” or “Why does this output tuple have such high probability?”. Second, the problem of determining the sensitive input tuples for the given query, e.g., users are interested to know the input tuples that can substantially alter the output, when their probabilities are modified (since they may be unsure about the input probability values). Existing systems provide the lineage/provenance of each of the output tuples in addition to the output probabilities, which is a boolean formula indicating the dependence of the output tuple on the input tuples. However, lineage does not immediately provide a quantitative relationship and it is not informative when we have multiple output tuples. In this paper, we propose a unified framework that can handle both the issues mentioned above to facilitate robust query processing. We formally define the notions of influence and explanations and provide algorithms to determine the top-ℓ influential set of variables and the top-ℓ set of explanations for a variety of queries, including conjunctive queries, probabilistic threshold queries, top-k queries and aggregation queries. Further, our framework naturally enables highly efficient incremental evaluation when input probabilities are modified (e.g., if uncertainty is resolved). Our preliminary experimental results demonstrate the benefits of our framework for performing robust query processing over probabilistic databases.

Abstract. Formal behavioral specifications written early in the system-design process and communicated across all design phases have been shown to increase the efficiency, consistency, and quality of the system under development. To prevent introducing design or verification errors, it is crucial to test specifications for satisfiability. Our focus here is on specifications expressed in linear temporal logic (LTL). We introduce a novel encoding of symbolic transition-based Büchi automata and a novel, “sloppy, ” transition encoding, both of which result in improved scalability. We also define novel BDD variable orders based on tree decomposition of formula parse trees. We describe and extensively test a new multi-encoding approach utilizing these novel encoding techniques to create 30 encoding variations. We show that our novel encodings translate to significant, sometimes exponential, improvement over the current standard encoding for symbolic LTL satisfiability checking. 1

We consider the problem of computing the probability of a Boolean function, which generalizes the model counting problem. Given an OBDD for such a function, its probability can be computed in linear time in the size of the OBDD. In this paper we investigate the connection between treewidth and the size of the OBDD. Bounded treewidth has proven to be applicable to many graph problems, which are NP-hard in general but become tractable on graphs with bounded treewidth. However, it is less well understood how bounded treewidth can be used for the probability computation problem of a Boolean function. We introduce a new notion of treewidth of a Boolean function, called the expression treewidth, as the smallest treewidth of any DAG-expression representing the function. Our new no-

the read-once property of branching programs and

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Abstract Tractable learning aims to learn probabilistic models where inference is guaranteed to be efficient. However, the particular class of queries that is tractable depends on the model and underlying representation. Usually this class is MPE or conditional probabilities Pr(x|y) for joint assignments x, y. We propose a tractable learner that guarantees efficient inference for a broader class of queries. It simultaneously learns a Markov network and its tractable circuit representation, in order to guarantee and measure tractability. Our approach differs from earlier work by using Sentential Decision Diagrams (SDD) as the tractable language instead of Arithmetic Circuits (AC). SDDs have desirable properties, which more general representations such as ACs lack, that enable basic primitives for Boolean circuit compilation. This allows us to support a broader class of complex probability queries, including counting, threshold, and parity, in polytime.

We present new results on the size of OBDD representations of structurally characterized classes of CNF formulas. First, we identify a natural sufficient condition, which we call the few subterms property, for a class of CNFs to have polynomial OBDD size; we then prove that CNFs whose incidence graphs are variable convex have few subterms (and hence have polynomial OBDD size), and observe that the few subterms property also explains the known fact that classes of CNFs of bounded treewidth have polynomial OBDD size. Second, we prove an exponential lower bound on the OBDD size of a family of CNF classes with incidence graphs of bounded degree, exploiting the combinatorial properties of expander graphs. 1

Treewidth measures the "tree-likeness" of structures. Many NP-complete problems, e.g., propositional satisfiability, are tractable on bounded-treewidth structures. In this work, we study the impact of treewidth bounds on QBF, a canonical PSPACE-complete problem. This problem is known to be fixed-parameter tractable if both the treewidth and alternation depth are taken as parameters. We show here that the function bounding the complexity in the parameters is provably nonelementary (assuming P is different than NP). This yields a strict hierarchy of fixed-parameter tractability inside PSPACE. As a tool for proving this result, we first prove a similar hierarchy for model checking QPTL, quantified propositional temporal logic. Finally, we show that QBF, restricted to instances with a slowly increasing (log # ) treewidth, is still PSPACE-complete.

Probabilistic database systems have successfully established themselves as a tool for managing uncertain data. However, much of the research in this area has focused on efficient query evaluation and has largely ignored two key issues that commonly arise in uncertain data management: First, how to provide explanations for query results, e.g., “Why is this tuple in my result? ” or “Why does this output tuple have such high probability?”. Second, the problem of determining the sensitive input tuples for the given query, e.g., users are interested to know the input tuples that can substantially alter the output, when their probabilities are modified (since they may be unsure about the input probability values). Existing systems provide the lineage/provenance of each of the output tuples in addition to the output probabilities, which is a boolean formula indicating the dependence of the output tuple on the input tuples. However, it does not immediately provide a quantitative relationship and it is not informative when we have multiple output tuples. In this paper, we propose a unified framework that can handle both the issues mentioned above and facilitate robust query processing. We formally define the notions of influence and explanations and provide algorithms to determine the top-ℓ influential set of variables and the top-ℓ set of explanations for a variety of queries, including conjunctive queries, probabilistic threshold queries, top-k queries and aggregation queries. Further, our framework naturally enables highly efficient, incremental evaluation when the input probabilities are modified, i.e., if the user decides to change the probability of an input tuple (e.g., if the uncertainty is resolved). Our preliminary experimental results demonstrate the benefits of our framework for performing robust query processing over probabilistic databases.